Answered: . Let ϕ : Z31 → Z31 be a homomorphism…

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. Let ϕ : Z31 → Z31 be a homomorphism such that ϕ(16) = 19. Calculate ϕ(1) and ϕ(10).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 15E: 15. Assume that can be written as the direct sum , where is a cyclic group of order . Prove that...

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Question

1. Let G = Z336 ⊕ Z12.

Find the external direct product of cyclic groups of prime power order that is isomorphic to G.

2. Let ϕ : Z31 → Z31 be a homomorphism such that ϕ(16) = 19. Calculate ϕ(1) and ϕ(10).

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